Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction

Optimized measurements for the susceptibility, self-energy, as well as three-leg and four-leg vertex functions are introduced for the continuous-time hybridization expansion quantum Monte Carlo solver for the impurity model in presence of a retarded interaction. The self-energy and vertex functions are computed from impurity averages which involve time integrals over the retarded interaction. They can be evaluated efficiently within the segment representation. These quantities are computed within dynamical mean-field theory in presence of plasmonic screening. In the antiadiabatic regime, the self-energy is strongly renormalized but retains features of the low energy scale set by the screened interaction. An explicit expression for its high-frequency behavior is provided. Across the screening-driven and interaction-driven metal-insulator transitions, the vertex functions are found to exhibit similar structural changes, which are hence identified as generic features of the Mott transition.